A comparative evaluation of books on mathematical modelling

AbstractIn this paper we present a comparative evaluation of books on mathematical modelling that have appeared in the last 15 years

Study of linear discrete time systems with state variable constraints

In this paper we discuss the property of reachability and controllability for a linear discrete time system, with the trajectory constrained to satisfy a state variable inequality constraint of the form

A model for population extinction

A new model is formulated for population changes, where the growth is deterministic and randomly occurring catastrophies cause reduction and possibly extinction of the population. Expressions for the mean time to extinction are presented

A note on mathematical models

Traditional undergraduate engineering and science courses do not give sufficient emphasis to mathematical model building. In this note we briefly discuss mathematical models and their construction

Optimal reliability choice in product design

In designing new products, the reliability of the product is an important variable. Greater reliability implies higher unit cost and hence higher selling price. The buyer’s decision to pay a higher price is influenced by the signaling mechanism which conveys information about product reliability. Product warranty is one such signal. The total sales depend on marketing variables such as selling price and warranty. The cost of servicing warranty depends on product reliability. This implies that decisions regarding product reliability at the design stage must be done in a framework which takes into account the marketing variables. In this paper, we develop a simple model which integrates marketing variables into the design phase and the reliability decisions are made jointly with marketing variables to maximize total profits

Controllability of a linear positive dynamic system

A positive dynamic system has the property that if the initial state is non-negative, then the state variable is non-negative for all future time. In this article, we study controllability of one such system with linear structure

A note on block replacement policy

In this note we study block replacement policy with a modification to include stock level at the beginning of the cycle

A stochastic model for service contract

When it is not economical to carry out maintenance in-house, out-sourcing to an external agent is an alternate viable option. In this paper, we study a simple maintenance service contract involving a single agent (providing the maintenance service) and a single customer (owner of the equipment and recipient of the maintenance service). We develop a simple model to obtain the optimal strategies for both the customer and the agent. We give a complete characterization of the strategies along with some sensitivity analysis and discuss some extensions